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Longest paths in digraphs

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Abstract

In this paper, we give a sufficient condition on the degrees of the vertices of a digraph to insure the existence of a path of given length, and we characterize the extremal graphs.

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References

  1. C. Berge, Graphs and hypergraphs, North Holland, Amsterdam, 1973.

    MATH  Google Scholar 

  2. J. C. Bermond, A. Germa, M. C. Heydemann andD. Sotteau, Chemins et circuits dans les graphes orientés, Proc. Coll. Montréal, 1979.Annals of Discrete Mathematics 8 (1980), 293–309.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. C. Bermond, On hamiltonian walks, Proc. 5th British Combinatorial Conference, Aberdeen, 1975,Congressus Numerantium 15,Utilitas Math. Publ., 41–51.

  4. J. C. Bermond andC. Thomassen, Cycles in digraphs, a survey,J. Graph Theory,5 (1981), 1–43.

    MATH  MathSciNet  Google Scholar 

  5. A. Ghouila-Houri, Flots et tensions dans un graphe,Ann. Scien. Ec. Norm. Sup.,81 (1964), 317–327.

    MathSciNet  Google Scholar 

  6. M. C. Heydemann,Thesis, Université Paris-Sud.

  7. M. C. Heydemann, On cycles and paths in digraphs,Discrete Math. 31 (1980), 217–219.

    Article  MATH  MathSciNet  Google Scholar 

  8. B. Jackson, Long paths and cycles in oriented graphs,J. Graph. Theory,5 (1981), 145–157,

    MATH  MathSciNet  Google Scholar 

  9. M. Las Vergnas, Sur les arborescences dans un graphe orientéDiscrete Math. 15 (1976), 27–39.

    Article  MATH  MathSciNet  Google Scholar 

  10. C. Thomassen, Long cycles in digraphs,Proc. London Math. Soc. to appear.

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Bermond, J.C., Germa, A., Heydemann, M.C. et al. Longest paths in digraphs. Combinatorica 1, 337–341 (1981). https://doi.org/10.1007/BF02579454

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  • DOI: https://doi.org/10.1007/BF02579454

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